krylov_matrix_market_example.cpp runs the symmetric/Hermitian Lanczos driver, including regular and transformed modes, on Matrix Market input.
krylov_nonsymmetric_matrix_market_example.cpp runs real nonsymmetric Arnoldi on Matrix Market input.
krylov_exponential_probe_example.cpp compares Krylov and Taylor exponential actions with exact synthetic references and estimator details.
krylov_exponential_orthogonality_example.cpp isolates the tolerance floor, basis orthogonality, and reorthogonalization behavior.
krylov_exponential_matrix_market_probe_example.cpp reproduces the TDVP harmonic-oscillator convergence case from tracked Matrix Market fixtures.

Several invocations are registered with CTest, including optional binary128 runs when MPLAPACK is configured. See the examples index, Krylov documentation, and Krylov test matrices.